Printed Lecture Notes

Here are the two chapters dealing with proof techniques. We will work on this subject during weeks 7 and 8

Chapters5&6.pdf

PowerPoint Presentations

Here are the PowerPoint files for this week.

Slides-week 6.pdf

I add the proof that the square root of a prime is irrational, as an example of a proof by contradiction

Please find as well the Google link (Links to an external site.)Links to an external site. to The School of Athen (by Raphael), used in the slides

Example of a proof by contrapositive and one by contradiction.pdf

Video Recordings

Lecture 11

Lecture 12

Short video: example of proving an implication with a direct proof

Clubs and strangers: brainstorming before getting a proof : before you get a well constructed proof, you need sometimes to brainstorm; do not think that all the proofs you read have been conceived straight away.

Clubs and strangers: putting all together. Here is an example of proof after the brainstorming. It is slightly different than the proof given in the lecture. You are not supposed to find such a proof, it is just given as an example.

Example of a proof by contradiction: $LaTeX: \sqrt{2}\in\mathbb{R}\setminus\mathbb{Q}$